Pointwise error estimate of the Legendre expansion: the known and unknown features

DOI10.1016/j.cma.2018.11.017zbMath1440.65027OpenAlexW2903275484WikidataQ128836652 ScholiaQ128836652MaRDI QIDQ1986826

Harri Hakula, Ivo M. Babuška

Publication date: 9 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2018.11.017

zbMATH Keywords

\(p\)-versionLegendre polynomialpointwise convergence

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Algorithms for approximation of functions (65D15)

Related Items (5)

Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation ⋮ Pointwise error estimates and local superconvergence of Jacobi expansions ⋮ Analysis of Error Localization of Chebyshev Spectral Approximations ⋮ Bernstein-type constants for approximation of \(| x |^\alpha\) by partial Fourier-Legendre and Fourier-Chebyshev sums ⋮ New error bounds for Legendre approximations of differentiable functions

Cites Work

• On the rate of convergence of Fourier-Legendre series of functions of bounded variation
• Spectral Methods
• On the Gibbs Phenomenon and Its Resolution
• Polynomial Approximation of Piecewise Analytic Functions
• On the convergence rates of Legendre approximation
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